Question

# Two cars start off to race with velocities 4 m/s and 2 m/s and travel in a straight line with uniform accelerations 1 m/s2 and 2 m/s2 respectively. If they reach the final point at the same time instant, then what is the length of the path?

A
12 m
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B
18 m
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C
24 m
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D
30 m
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Solution

## The correct option is C 24 mLet the two cars be car A and car B. For car A: s1=ut+12at2⇒s1=4t+12×1×t2 (using second equation of motion) For car B: s2=ut+12at2⇒s2=2t+12×2×t2 (using second equation of motion) On equating the distance, s1=s2 ⇒4t+12×1×t2=2t+12×2×t2 ⇒2t=t22 ⇒t=4 s Putting the value in any one of the equations, we get s=4×4+12×1×42=24 m Alternate Solution: Initial velocity of 1st car w.r.t. 2, u12=4−2=2 m/s Acceleration of 1st car w.r.t. 2, a12=1−2=−1 m/s2 Finally, displacement of 1st car w.r.t 2, S12=0 Using second equation of motion, S12=u12+12a12t2 ⇒0=2t−12×1×t2⇒t=4 s ∴ Distance travelled by 1st car =ut+12at2 =4×4+12×1×42=24 m

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